The Time-Dependent Schrödinger Equation, Riccati Equation, and Airy Functions by Nathan A. Lanfear, Sergei K. Suslov

“…We construct the Green functions (or Feynman’s propagators) for the Schrödinger equations of the form <inline-formula data-eusoft-scrollable-element="1"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" data-eusoft-scrollable-element="1"><semantics data-eusoft-scrollable-element="1"><mrow data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">i</mi><msub data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">ψ</mi><mi data-eusoft-scrollable-element="1">t</mi></msub><mo data-eusoft-scrollable-element="1">+</mo><mstyle scriptlevel="0" displaystyle="true" data-eusoft-scrollable-element="1"><mfrac data-eusoft-scrollable-element="1"><mn data-eusoft-scrollable-element="1">1</mn><mn data-eusoft-scrollable-element="1">4</mn></mfrac></mstyle><msub data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">ψ</mi><mrow data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">x</mi><mi data-eusoft-scrollable-element="1">x</mi></mrow></msub><mo data-eusoft-scrollable-element="1">±</mo><mi data-eusoft-scrollable-element="1">t</mi><msup data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">x</mi><mn data-eusoft-scrollable-element="1">2</mn></msup><mi data-eusoft-scrollable-element="1">ψ</mi><mo data-eusoft-scrollable-element="1">=</mo><mn data-eusoft-scrollable-element="1">0</mn></mrow></semantics></math></inline-formula> (for the wave function <inline-formula data-eusoft-scrollable-element="1"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" data-eusoft-scrollable-element="1"><semantics data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">ψ</mi></semantics></math></inline-formula> and its time (<i data-eusoft-scrollable-element="1">t</i>) and <i data-eusoft-scrollable-element="1">x</i>-space derivatives) in terms of Airy functions and solve the Cauchy initial value problem in the coordinate and momentum representations. …”
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Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions by Gangadharan Murugusundaramoorthy, Luminita-Ioana Cotîrlă, Daniel Breaz, Sheza M. El-Deeb

“…The Lucas balancing polynomial is linked to a family of bi-starlike functions denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">S</mi><mrow><mi>s</mi><mi>c</mi></mrow><mi>c</mi></msubsup><mrow><mo>(</mo><mi>ϑ</mi><mo>,</mo><mo>Ξ</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, which we present and examine in this work. …”
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On Estimates of Functions in Norms of Weighted Spaces in the Neighborhoods of Singularity Points by Viktor A. Rukavishnikov, Elena I. Rukavishnikova

“…It is necessary to have estimates of the function norms in the neighborhood of the singularity point to study the existence and uniqueness of the <inline-formula data-eusoft-scrollable-element="1"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" data-eusoft-scrollable-element="1"><semantics data-eusoft-scrollable-element="1"><msub data-eusoft-scrollable-element="1"><mi data-eusoft-scrollable-element="1">R</mi><mi data-eusoft-scrollable-element="1">ν</mi></msub></semantics></math></inline-formula>-generalized solution, its coercive and differential properties of biharmonic boundary value problems with a corner singularity. …”
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Symmetry and Quantum Calculus in Defining New Classes of Analytic Functions by Fuad Alsarari, Abdulbasit Darem, Muflih Alhazmi, Alaa Awad Alzulaibani

“…This paper introduces a novel class of analytic functions that integrates <i>q</i>-calculus, Janowski-type functions, and (<i>a</i>, <i>b</i>)-symmetrical functions. …”
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Functioning of Literary Anthroponyms in the Works by E. Canetti and K. Hoffer by E. M. Shastina, J. K. Kazakova

“…The authors dwell on the study of the functioning of literary anthroponyms in the text space of works. …”
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Systemic arterial hypertension and cognition in adults: effects on executive functioning by Natália Cristina MORAES, Henrique Cotchi Simbo MUELA, Claudia Maia MEMÓRIA, Valéria Aparecida da COSTA-HONG, Michel Ferreira MACHADO, Mario Amore CECHINHI, Ricardo NITRINI, Luiz Aparecido BORTOLOTTO, Monica Sanches YASSUDA

“…The objective of this study was to investigate the relation between SAH and the components of executive functions (EF), inhibitory control (IC), updating and shifting, comparing a control group (without SAH) to patients with SAH, in two levels of severity. …”
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FUNCTIONAL AND TRANSLATIONAL SPECIFICS OF POETIC TEXT AS AESTHETIC SENSE VERBALIZATION by Natalya Nagamova, Irina Chepurina

“…The article discusses the general principles of aesthetics verbalization in the poetic text as a form of literary discourse, which allows a fictional sense to exist and function in poetic compositions, and the ways of its interpretation and decoding by the receptor. …”
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The Interplay Between Loss Functions and Structural Constraints in Dependency Parsing by Robin Kurtz, Marco Kuhlmann

“…Several of the decoding algorithms that have been applied to this task employ structural restrictions on candidate solutions, such as the restriction to projective dependency trees in syntactic parsing, or the restriction to noncrossing graphs in semantic parsing. In this paper we study the interplay between structural restrictions and a common loss function in neural dependency parsing, the structural hingeloss. …”
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Uncovering the functional aspect of translator style: corpus stylistic insights by Kan Wu

“…This involves an examination of how the translators render thematic words and handle the resulting lexico-semantic patterns. The findings reveal notable disparities in the translators’ functional styles, which are influenced by multiple translatorial and extra-translatorial factors, including the translators’ backgrounds, motivations, preferences, interpretation, patronage, and technological development. …”
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Assessment of language abilities and functionality in adults and elders with Down syndrome by Cláudia Lopes Carvalho, Orestes Vicente Forlenza, Marcia Radanovic

“…Conclusion Functional performance was associated with different linguistic tasks in the literate (verbal memory and executive functions) and non-literate (verbal memory and lexico-semantic process) groups.…”
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Patio as a Constant in Language, Culture and Architecture: Meanings and Functions by O. A. Saprykina

“…The patio is known in the East and in the West, although it has different forms, functions and linguistic representation everywhere. …”
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Entre sémantique lexicale et sémantique textuelle : une analyse lexicale et stylistique de Before I Say Goodbye de Ruth Picardie by Catherine Paulin

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Soft Classification in a Composite Source Model by Yuefeng Cao, Jiakun Liu, Wenyi Zhang

Subjects: “…indirect rate–distortion function…”
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On Value Distribution for the Mellin Transform of the Fourth Power of the Riemann Zeta Function by Virginija Garbaliauskienė, Audronė Rimkevičienė, Mindaugas Stoncelis, Darius Šiaučiūnas

“…In this paper, the asymptotic behavior of the modified Mellin transform <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">Z</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>=</mo><mi>σ</mi><mo>+</mo><mi>i</mi><mi>t</mi></mrow></semantics></math></inline-formula>, of the fourth power of the Riemann zeta function is characterized by weak convergence of probability measures in the space of analytic functions. …”
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A Short Note on Fractal Interpolation in the Space of Convex Lipschitz Functions by Fatin Gota, Peter Massopust

“…In this short note, we consider fractal interpolation in the Banach space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>V</mi><mi>θ</mi></msup><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of convex Lipschitz functions defined on a compact interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>⊂</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>. …”
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A Class of the Generalized Ramanujan Tau Numbers and Their Associated Partition Functions by Aleksandar Petojević, Hari M. Srivastava, Sonja Orlić

“…The authors consider the associated partition functions and derive connections of the Eisenstein series with the numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mi>s</mi></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. …”
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Efficient Numerical Quadrature for Highly Oscillatory Integrals with Bessel Function Kernels by Guo He, Yuying Liu

“…For one of these integrals, we reformulate the Bessel function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>ν</mi></msub><mrow><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> as a linear combination of the modified Bessel function of the second kind <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mi>ν</mi></msub><mrow><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>, subsequently transforming it into a line integral over an infinite interval on the complex plane. …”
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Deviations from Normality in Autocorrelation Functions and Their Implications for MA(q) Modeling by Manuela Royer-Carenzi, Hossein Hassani

“…The Autocorrelation Function (ACF) is commonly used to identify the order <i>q</i> of Moving Average (MA(<i>q</i>)) models, as it theoretically vanishes for lags beyond <i>q</i>. …”
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Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions by David Levin, Nira Gruberger

“…Given function values on a uniform grid over a domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>, we present a novel B-spline-based approximation framework, using new adaptable quasi-interpolation operators. …”
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Robust Discontinuity Indicators for High-Order Reconstruction of Piecewise Smooth Functions by Yipeng Li, Qiao Chen, Xiangmin Jiao

“…The accurate reconstruction of piecewise continuous functions on meshes is challenging due to potential spurious oscillations—namely the <i>Gibbs phenomenon</i>—especially for high-order methods. …”
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